Question:
Two positive integers a and $b$ can be written as $a=x^{3} y^{2}$ and $b=x y^{3}$, where $x$ and $y$ are prime numbers. Find $\operatorname{HCF}(a, b)$ and $L C M(a, b)$.
Solution:
It is given that, $a=x^{3} y^{2}$ and $b=x y^{3}$, where $x$ and $y$ are prime numbers.
$\mathrm{LCM}(a, b)=\mathrm{LCM}\left(x^{3} y^{2}, x y^{3}\right)$
$=$ The highest of indices of $x$ and $y$
$=x^{3} y^{3}$
$\operatorname{HCF}(a, b)=\operatorname{HCF}\left(x^{3} y^{2}, x y^{3}\right)$
$=$ The lowest of indices of $x$ and $y$
$=x y^{2}$
Hence, $\operatorname{HCF}(a, b)=x y^{2}$ and $\operatorname{LCM}(a, b)=x^{3} y^{3}$.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.